The only outstanding quantity that remains unknown is the voltage across capacitor that is given as:

VC = V – VL = 10 ∠0o – 17.5 ∠36.3o

The evaluation of VC requires VL expressed in the complex terms from below figure gives:

Figure: Argand Diagram for VL

a = Real(VL) = |VL|cosΦL

jb = Imag (VL) = j|VL|sinΦL

VL = |VL| cosΦL + j|VL|sinΦL

VL = 17.5 cos 36.3 + j 17.5 sin 36.3

Then,

VL = 17.5 x 0.8059 + j17.5 x 0.5920

VL = 14.1 + j 10.36

Then,

VC = V – VL = 10 - 14.1 – j10.36 = - 4.1- j10.36

And hence finally:

|V| = √ (4.1)2 + (10.36)2 = 11.14 V

∠ΦC = Tan-1 (-10.36/-4.1) = 68.4o – 180o = -111.6o

The fact that both real and imaginary coefficients of VC are negative should be accounted for which is done by comprising the -180o rotation to place this vector in third quadrant. The whole phasor diagram exhibiting all currents and voltages is given in figure shown below.

Figure: A Complete Phasor Diagram for the Circuit of first figure

Kirchhoff’s Laws:

Kirchoff’s laws can be applied to the ac circuits in a similar way to dc circuits. The major difference is that the sources and impedances encompass to be treated as the complex quantities. The values for currents and voltages and can be computed as complex quantities first and transformed into the form of phase and magnitude at the end. Consider the circuit shown in figure below where the frequency and component values have been selected to give round figures for the values of reactance. Such can then be treated as purely imaginary impedances. Such circuit is analysed by using Nodal Analysis by applying the Kirchhoff’s Current Law to node(s) of interest.

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